TY - JOUR
T1 - Metrics on semistable and numerically effective Higgs bundles
JF - J. Reine Angew. Math. 612 (2007) 59-79
Y1 - 2007
A1 - Ugo Bruzzo
A1 - Beatriz Grana-Otero
AB - We consider fibre metrics on Higgs vector bundles on compact K\\\\\\\"ahler manifolds, providing notions of numerical effectiveness and numerical flatness in terms of such metrics. We prove several properties of bundles satisfying such conditions and in particular we show that numerically flat Higgs bundles have vanishing Chern classes, and that they admit filtrations whose quotients are stable flat Higgs bundles. We compare these definitions with those previously given in the case of projective varieties. Finally we study the relations between numerically effectiveness and semistability, providing semistability criteria for Higgs bundles on projective manifolds of any dimension.
UR - http://hdl.handle.net/1963/1840
U1 - 2376
U2 - Mathematics
U3 - Mathematical Physics
ER -